Compute with scientific notation

This lesson will show you how to compute with scientific notation. You will learn to add, subtract, multiply, and divide with scientific notation.

It is important to understand how to convert numbers to scientific notation before starting this lesson.

Add and subtract with scientific notation
Example #1:

Add and subtract 2 × 105 + 4 × 103 and -6 × 105 + 2 × 103 + 9 × 104

When adding or subtracting numbers in scientific notation, you can only add or subtract numbers that have the same exponent. Therefore, first step is to put the ones with the same exponent together.

Addition: 2 × 105 + 4 × 103+ -6 × 105 + 2 × 103 + 9 × 104

(2 × 105 + -6 × 105) + (4 × 103 + 2 × 103) + 9 × 104

Add the numbers you see on the left of 105.This is the number before the multiplication sign. Then, put the sum next to 105 and put the multiplication sign between the sum and 105 . Do the same thing for 103

2 + -6 = -4 and 4 + 2 = 6

2 × 105 + 4 × 103+ -6 × 105 + 2 × 103 = -4 × 105 + 6 × 103 + 9 × 104

Subtraction: 2 × 105 + 4 × 103- ( -6 × 105 + 2 × 103 + 9 × 104 )

2 × 105 + 4 × 103- -6 × 105- +2 × 103- +9 × 104

2 × 105 + 4 × 103 + 6 × 105 - 2 × 103 - 9 × 104

(2 × 105 + 6 × 105) + (4 × 103 - 2 × 103) - 9 × 104

Add the numbers you see on the left of 105 and put the answer next to 105.

Subtract the numbers you see on the left of 103 and put the answer next to 103.